Math Help - triangular matrix

1. triangular matrix

if i have a matrix A how do i put it in upper triangular form??

2. upper triangular form means that below the diagonal you have only zeros.

to do that, you just need to apply elementary row operations to scale the matrix.

3. arh let me refine my question if i have matrix A,

PA(P^-1)=B , where B is upper triangular matrix, but what is P?

i realised P contains eigenvectors as columns. but i stumble up as P has no inverse and it drives me mad and now im going to bed.

4. Are you talking about finding the Jordan Canonical Form of the matrix? If your working over a field that contains all of the eigenvalues of the matrix (the complex numbers are algebraicly closed, so this is a good one to work in) you can represent the matrix into one that is zero everywhere except possibly the diagonal and 1st superdiagonal.

The matrix P consists of the basis for the eigenspace of each of the Jordan blocks. In particular if you have all distinct eigenvalues, each eigenspace is one dimensional and your P matrix is just the corresponding eigenvectors and it will transform it into a diagonal matrix with the eigenvalues on the diagonal.

Not really sure if this is what you are talking about, but hope it helps.